JEE PYQ: Ray Optics Question 33
Question 33 - 2019 (08 Apr Shift 1)
In figure, the optical fiber is $l = 2$ m long and has a diameter of $d = 20$ $\mu$m. If a ray of light is incident on one end of the fiber at angle $\theta_1 = 40°$, the number of reflections it makes before emerging from the other end is close to: (refractive index of fiber is 1.31 and $\sin 40° = 0.64$)
(1) 55000
(2) 66000
(3) 45000
(4) 57000
Show Answer
Answer: (4)
Solution
Using Snell’s law of refraction, $1 \times \sin 40° = 1.31 \sin\theta$ $\Rightarrow \sin\theta = \frac{0.64}{1.31} = 0.49 \approx 0.5$ $\Rightarrow \theta = 30°$ $x = 20$ $\mu$m $\times \cot\theta$ $\therefore$ Number of reflections $= \frac{2}{20 \times 10^{-6} \times \cot\theta}$ $= \frac{2 \times 10^6}{20 \times \sqrt{3}} = 57735 \approx 57000$
BETA
